Overview
- Group
- SmallGroup(1152,98805)
- Rank
- 4
- Schläfli Type
- {2,12,24}
- Vertices, edges, …
- 2, 12, 144, 24
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)( 29, 34)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)( 46, 53)( 47, 52)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 75,129)( 76,131)( 77,130)( 78,135)( 79,137)( 80,136)( 81,132)( 82,134)( 83,133)( 84,138)( 85,140)( 86,139)( 87,144)( 88,146)( 89,145)( 90,141)( 91,143)( 92,142)( 93,111)( 94,113)( 95,112)( 96,117)( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)(104,121)(105,126)(106,128)(107,127)(108,123)(109,125)(110,124);; s2 := ( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,124)( 40,123)( 41,125)( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,133)( 58,132)( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)( 66,142)( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)( 74,146);; s3 := ( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)(127,146)(128,145);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(146)!(1,2); s1 := Sym(146)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 21, 30)( 22, 32)( 23, 31)( 24, 36)( 25, 38)( 26, 37)( 27, 33)( 28, 35)( 29, 34)( 39, 48)( 40, 50)( 41, 49)( 42, 54)( 43, 56)( 44, 55)( 45, 51)( 46, 53)( 47, 52)( 58, 59)( 60, 63)( 61, 65)( 62, 64)( 67, 68)( 69, 72)( 70, 74)( 71, 73)( 75,129)( 76,131)( 77,130)( 78,135)( 79,137)( 80,136)( 81,132)( 82,134)( 83,133)( 84,138)( 85,140)( 86,139)( 87,144)( 88,146)( 89,145)( 90,141)( 91,143)( 92,142)( 93,111)( 94,113)( 95,112)( 96,117)( 97,119)( 98,118)( 99,114)(100,116)(101,115)(102,120)(103,122)(104,121)(105,126)(106,128)(107,127)(108,123)(109,125)(110,124); s2 := Sym(146)!( 3, 79)( 4, 78)( 5, 80)( 6, 76)( 7, 75)( 8, 77)( 9, 82)( 10, 81)( 11, 83)( 12, 88)( 13, 87)( 14, 89)( 15, 85)( 16, 84)( 17, 86)( 18, 91)( 19, 90)( 20, 92)( 21,106)( 22,105)( 23,107)( 24,103)( 25,102)( 26,104)( 27,109)( 28,108)( 29,110)( 30, 97)( 31, 96)( 32, 98)( 33, 94)( 34, 93)( 35, 95)( 36,100)( 37, 99)( 38,101)( 39,124)( 40,123)( 41,125)( 42,121)( 43,120)( 44,122)( 45,127)( 46,126)( 47,128)( 48,115)( 49,114)( 50,116)( 51,112)( 52,111)( 53,113)( 54,118)( 55,117)( 56,119)( 57,133)( 58,132)( 59,134)( 60,130)( 61,129)( 62,131)( 63,136)( 64,135)( 65,137)( 66,142)( 67,141)( 68,143)( 69,139)( 70,138)( 71,140)( 72,145)( 73,144)( 74,146); s3 := Sym(146)!( 4, 5)( 7, 8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 21, 30)( 22, 32)( 23, 31)( 24, 33)( 25, 35)( 26, 34)( 27, 36)( 28, 38)( 29, 37)( 40, 41)( 43, 44)( 46, 47)( 49, 50)( 52, 53)( 55, 56)( 57, 66)( 58, 68)( 59, 67)( 60, 69)( 61, 71)( 62, 70)( 63, 72)( 64, 74)( 65, 73)( 75, 93)( 76, 95)( 77, 94)( 78, 96)( 79, 98)( 80, 97)( 81, 99)( 82,101)( 83,100)( 84,102)( 85,104)( 86,103)( 87,105)( 88,107)( 89,106)( 90,108)( 91,110)( 92,109)(111,129)(112,131)(113,130)(114,132)(115,134)(116,133)(117,135)(118,137)(119,136)(120,138)(121,140)(122,139)(123,141)(124,143)(125,142)(126,144)(127,146)(128,145); poly := sub<Sym(146)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;